CS 726: Nonlinear Optimization I
Fall 2015 (also ISyE, Stat, Math)
Michael C. Ferris
- Office: 4381 CS&S
- Telephone: 262-4281
- E-mail: I will not respond to questions about class material via
email. We will use Piazza for this.
- Office Hours: 12:00 - 1:00 Mondays, 11:00 - 12:00 Wednesdays
- 9:55 - 10:45 MWF, 2540 Eng Hall
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|Course URL ||http://www.cs.wisc.edu/~cs726-1
General Course Information (http://www.cs.wisc.edu/~ferris/cs726.html)
Theory and algorithms for nonlinear optimization, focusing on unconstrained optimization. Line-search and trust-region methods; quasi-Newton methods; conjugate-gradient and limited-memory methods for large-scale problems; derivative-free optimization; algorithms for least-squares problems and nonlinear equations; gradient projection algorithms for bound-constrained problems; and simple penalty methods for nonlinearly constrained optimization.
- Continuous optimization paradigms
- Representative applications
- Mathematical background, including convex sets and functions
- Unconstrained optimization: Theory and algorithms
- Optimality conditions
- Gradient methods and Newton's method
- Line search methods
- Quasi-Newton methods
- Derivative-Free optimization
- Model-based methods
- Pattern-search methods
- Large-scale unconstrained optimization:
- Conjugate gradient methods (linear and nonlinear)
- Limited-memory quasi-Newton methods
- Nonlinear equations and least-squares problems
- Optimization with bound constraints:
- Projections and gradient projection algorithms
- Enhancements of gradient projection using second-order information and quasi-Newton techniques.
- Constrained nonlinear programming algorithms
- Constraint elimination
- Penalty methods
- I will use a set of notes specially prepared for this course.
They will cover the first part of the Nocedal and Wright book.
- Numerical Optimization, J. Nocedal and S.J. Wright,
Springer Series in Operations Research, Springer-Verlag, New York,
2006 (2nd edition).
Convex Optimization, S. Boyd and L. Vandenberghe,
Cambridge University Press, UK 2004.
- Nonlinear Optimization, Andrzej Ruszczynski,
Princeton University Press, NJ 2006.
- Nonlinear Programming, 2nd Edition, Dimitri Bertsekas,
Athena Scientific, Belmont, MA 1999.
- Practical Methods of Optimization, 2nd Edition, R. Fletcher,
- Practical Optimization, P. Gill, W. Murray and M. Wright,
Academic Press, 1981.
- Nonlinear Programming Theory and Algorithms , M. S. Bazaraa, H. D. Sherali and C. M. Shetty,
Second Edition, Wiley, New York 2006.
The MATLAB PRIMER (Third Edition): An introduction to the
basic commands and utilities that you may need in Matlab.
Programming Assignments and Homeworks
All assignments need to be written up entirely separately.
You may discuss the problems informally with others in the class, but the
discussions must not include code or explicit solutions to any of
- N Assignments total.
Most homeworks will be handed in either in hard copy or using the drop box facility of Learn@UW. The drop box menu is found in the top menu bar once you have logged into the system.
Most of the assignments will
require the use of MATLAB, which will also be used extensively in the
No homework or project accepted in mailbox of instructor.
Further details will be provided when the assignments are passed out.
Homework due at beginning of class one week after assigned unless otherwise noted.
Examinations are closed book, with the exception that 1
handwritten sheet (standard size paper) can be brought in to the examination.
- Midterm Examination: Monday October 12 at 7:15 - 9:15pm in EH 2535.
- Final Examination -
Monday, December 21 at 10:05 am - 12:05 pm
in 1221 CS.
Previous exams (from 730) are given below, relevant questions are:
2003 (Q1), 2004 (Q2), 2005 (Q1)
Final Exam 2003
Final Exam 2004
Final Exam 2005
Final Exam 2009
Final Exam 2011
- Prereq: Familiarity with basic analysis (e.g. Math 521) and either Math 443 or 320, or consent of instructor
CS Department Computing Information
This page was updated September 2, 2015.